@conference {928,
	title = {Detecting critical points in 2D scalar field ensembles using Bayesian inference},
	booktitle = {2022 IEEE 15th Pacific Visualization Symposium (PacificVis)},
	year = {2022},
	month = {April},
	abstract = {In an era of quickly growing data set sizes, information reduction methods such as extracting or highlighting characteristic features become more and more important for data analysis. For single scalar fields, topological methods can fill this role by extracting and relating critical points.  While such methods are regularly employed to study single scalar fields, it is less well studied how they can be extended to uncertain data, as produced, e.g., by ensemble simulations.

Motivated by our previous work on visualization in climate research, we study new methods to characterize critical points in ensembles of 2D scalar fields. Previous work on this topic either assumed or required specific distributions, did not account for uncertainty introduced by approximating the underlying latent distributions by a finite number of fields, or did not allow to answer all our domain experts{\textquoteright} questions. In this work, we use Bayesian inference to estimate the probability of critical points, either of the original ensemble or its bootstrapped mean. This does not make any assumptions on the underlying distribution and allows to estimate the sensitivity of the results to finite-sample approximations of the underlying distribution. We use color mapping to depict these probabilities and the stability of their estimation. The resulting images can, e.g., be used to estimate how precise the critical points of the mean-field are. We apply our method to synthetic data to validate its theoretical properties and compare it with other methods in this regard. We also apply our method to the data from our previous work, where it provides a more accurate answer to the domain experts{\textquoteright} research questions.},
	doi = {10.1109/PacificVis53943.2022.00009},
	author = {Vietinghoff, Dominik and B{\"o}ttinger, Michael and Scheuermann, Gerik and Heine, Christian}
}
@conference {908,
	title = {An Extension of Empirical Orthogonal Functions for the Analysis of Time-Dependent 2D Scalar Field Ensembles},
	booktitle = {2021 IEEE 14th Pacific Visualization Symposium (PacificVis)},
	year = {2021},
	month = {April},
	abstract = {To assess the reliability of weather forecasts and climate simulations, common practice is to generate large ensembles of numerical simulations. Analyzing such data is challenging and requires pattern and feature detection. For single time-dependent scalar fields, empirical orthogonal functions (EOFs) are a proven means to identify the main variation. In this paper, we present an extension of that concept to time-dependent ensemble data. We applied our methods to two ensemble data sets from climate research in order to investigate the North Atlantic Oscillation (NAO) and East Atlantic (EA) pattern.},
	doi = {10.1109/PacificVis52677.2021.00014},
	author = {Vietinghoff, Dominik and Heine, Christian and B{\"o}ttinger, Michael and Scheuermann, Gerik}
}
@article {883,
	title = {Towards Modeling Visualization Processes as Dynamic Bayesian Networks},
	journal = {IEEE Transactions on Visualization and Computer Graphics},
	volume = {27},
	year = {2021},
	pages = {1000-1010},
	issn = {1077-2626},
	doi = {10.1109/TVCG.2020.3030395},
	author = {Heine, Christian}
}
@conference {907,
	title = {Visual Analysis of Spatio-Temporal Trends in Time-Dependent Ensemble Data Sets on the Example of the North Atlantic Oscillation},
	booktitle = {2021 IEEE 14th Pacific Visualization Symposium (PacificVis)},
	year = {2021},
	month = {April},
	abstract = {A driving factor of the winter weather in Western Europe is the North Atlantic Oscillation (NAO), manifested by fluctuations in the difference of sea level pressure between the Icelandic Low and the Azores High. Different methods have been developed that describe the strength of this oscillation, but they rely on certain assumptions, e.g., fixed positions of these two pressure systems. It is possible that climate change affects the mean location of both the Low and the High and thus the validity of these descriptive methods. This study is the first to visually analyze large ensemble climate change simulations (the MPI Grand Ensemble) to robustly assess shifts of the drivers of the NAO phenomenon using the uncertain northern hemispheric surface pressure fields. For this, we use a sliding window approach and compute empirical orthogonal functions (EOFs) for each window and ensemble member, then compare the uncertainty of local extrema in the results as well as their temporal evolution across different CO2 scenarios. We find systematic northeastward shifts in the location of the pressure systems that correlate with the simulated warming. Applying visualization techniques for this analysis was not straightforward; we reflect and give some lessons learned for the field of visualization.},
	doi = {10.1109/PacificVis52677.2021.00017},
	author = {Vietinghoff, Dominik and Heine, Christian and B{\"o}ttinger, Michael and Maher, Nicola and Jungclaus, Johann and Scheuermann, Gerik}
}
@article {829,
	title = {Modeling How Humans Judge Dot-Label Relations in Point Cloud Visualizations},
	journal = {IEEE Transactions on Visualization and Computer Graphics},
	volume = {26},
	year = {2020},
	pages = {2144-2155},
	doi = {10.1109/TVCG.2020.2970509},
	author = {Reckziegel, Martin and Pfeiffer, Linda and Heine, Christian and J{\"a}nicke, Stefan}
}
@conference {939,
	title = {Topological Subdivision Graphs for Comparative and Multifield Visualization},
	booktitle = {Topological Methods in Data Analysis and Visualization V},
	year = {2020},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Cham},
	abstract = {We propose that a topological model of a real-valued function can be employed to define a spatial subdivision of the function{\textquoteright}s domain. When multiple topologically-induced subdivisions for the same or different functions on the same domain are combined, a finer spatial subdivision arises: the topological subdivision complex. The topological subdivision graph then gives adjacency relations among the d-cells of the subdivision complex and can be used to describe similarities among topological models. We apply this idea to give new topological models for multiple real-valued functions (multifields), extending contour trees and Morse-Smale complexes to these problem settings, and we illustrate our idea for piecewise-linear functions. We also discuss how our work relates to joint contour nets.},
	isbn = {978-3-030-43036-8},
	author = {Heine, Christian and Garth, Christoph},
	editor = {Carr, Hamish and Fujishiro, Issei and Sadlo, Filip and Takahashi, Shigeo}
}
@article {830,
	title = {A Survey of Topology-based Methods in Visualization},
	journal = {Computer Graphics Forum},
	volume = {35},
	year = {2016},
	month = {06/2016},
	chapter = {643-667},
	doi = {10.1111/cgf.12933},
	author = {Heine, Christian and Leitte, Heike and Hlawitschka, Mario and Iuricich, Federico and De Floriani, Leila and Scheuermann, Gerik and Hagen, Hans and Garth, Christoph}
}
@proceedings {619,
	title = {Vortex Detection in 4DMRI Data: Using Proper Orothogonal Decomposition for Improved Noise Robustness},
	year = {2014},
	pages = {127-131},
	author = {Carnecky, Robert and Brunner, Thomas and Born, Silvia and Waser, J{\"u}rgen and Heine, Christian and Ronny Peikert}
}
